Benchmarking State-of-the-Art Theory and Empirical Models of Pionless Neutrino-Argon Scattering in GENIE

This paper utilizes the GENIE event generator to benchmark state-of-the-art theoretical and empirical models of pionless neutrino-argon scattering against recent MicroBooNE experimental data, evaluating the performance of sophisticated theoretical components against empirically-driven alternatives.

The Gist

Imagine you are trying to predict exactly how a billiard ball will bounce off a cluster of other balls on a table. In the world of physics, scientists use complex computer programs (called "event generators") to simulate these collisions. One of the most popular programs is called GENIE. It's like the "Google Maps" for neutrino experiments, helping researchers predict where particles will go when they smash into atoms.

However, just like a GPS can get lost if the map data is slightly off, GENIE needs to be constantly updated and tested against real-world data to make sure its predictions are accurate.

This paper is essentially a quality control report for GENIE. The authors took the latest version of the software and tested it against real data collected by the MicroBooNE experiment, which shoots neutrinos (ghostly, tiny particles) into a tank of liquid argon.

Here is a breakdown of what they did and what they found, using simple analogies:

1. The "Recipe" Problem

Think of the GENIE software as a giant, modular recipe book for making a "neutrino collision simulation." The recipe has several key ingredients:

• The Nuclear Model: How the "target" (the argon atom) is structured. Is it a solid block, or a loose cloud of particles?
• The Form Factor: A mathematical rule describing how the particles inside the atom react when hit.
• The Final State Interaction (FSI): What happens after the hit? Do the pieces bounce around inside the atom and lose energy, or do they fly out cleanly?

The authors wanted to see which combination of ingredients produced a simulation that looked most like the real data from MicroBooNE. They treated the software like a "mix-and-match" kit, swapping out one ingredient at a time to see which one improved the taste of the final dish.

2. The "Theoretical" vs. "Empirical" Debate

The paper compares two types of ingredients:

• The "Empirical" (Real-World) Ingredients: These are based on fitting the math to past experiments. They are like using a recipe that worked perfectly for your grandmother's cake because she tweaked it over 50 years.
• The "Theoretical" (First-Principles) Ingredients: These are based on deep, complex physics calculations (like Lattice QCD) that try to calculate the laws of nature from scratch. This is like trying to bake a cake by calculating the exact chemical reaction of every molecule of flour and sugar.

The Surprise: Usually, scientists hope that the "Theoretical" (deep math) ingredients will win because they are more "pure." However, in this study, the Empirical ingredients actually performed better. The "Grandma's Recipe" (data-driven models) matched the real-world data much more closely than the "Calculated Recipe" (pure theory).

3. The "Bug" Discovery

While testing, the authors found a hidden bug in the code.

• The Analogy: Imagine a recipe that says "add 1 cup of flour," but the measuring cup the chef is using is actually slightly smaller than a real cup. For a long time, nobody noticed because the difference was small.
• The Reality: The software had been slightly underestimating the number of collisions for a specific type of model. The authors fixed this code error. Interestingly, fixing the bug made a big difference for one type of nuclear model (the "Spectral Function" model) but barely changed the other (the "Local Fermi Gas" model).

4. The Results: What Worked Best?

After running hundreds of simulations and comparing them to the MicroBooNE data, they found the "Golden Combination" that fit the data best:

1. The Nuclear Model: A standard, data-driven model (Local Fermi Gas) worked just as well as the more complex theoretical one.
2. The Form Factor: A new calculation based on Lattice QCD (a super-advanced computer simulation of quantum physics) worked better than the old standard based on neutrino-deuterium data. This was a major finding: the new, high-tech math for the particle's shape was the key to getting the numbers right.
3. The Final State: The older, simpler "Empirical" model for how particles bounce around inside the atom (hA2018) worked much better than the newer, more complex "Theoretical" model (INCL).

5. Why Does This Matter?

The paper concludes that for the upcoming giant neutrino experiments (like DUNE), we shouldn't just blindly trust the most complex, "state-of-the-art" theoretical models. Instead, we need to be careful about mixing and matching.

The best simulation they built wasn't the one with the most "fancy" theoretical parts. It was a hybrid:

• It used the new, high-tech math for the particle's shape (Lattice QCD).
• But it used the proven, data-driven rules for how the atom is built and how the pieces bounce around afterwards.

In short: The paper is a guide for physicists on how to tune their "neutrino simulators." They found that while some new, fancy theoretical tools are excellent, the best results come from sticking with proven, real-world data for the messy parts of the collision, while using the new math only where it truly shines. They also fixed a hidden bug that was making some predictions slightly too low.

Technical Summary

Problem Statement
Upcoming neutrino oscillation experiments, such as DUNE, Hyper-Kamiokande, and JUNO, require improved simulations of neutrino scattering to achieve the necessary resolution. Current experiments, including MicroBooNE, are providing high-quality data on neutrino-argon scattering that challenge existing cross-section calculations. Specifically, the mean energy of the MicroBooNE Booster Neutrino Beam ($\sim$800 MeV) makes the experiment primarily sensitive to nuclear models and reaction models for quasielastic (QE) and 2-particle–2-hole (2p2h, or meson exchange current, MEC) processes. While "QE-like" data (pionless, CC0$\pi$ final states) are typically used to isolate these processes, previous comparisons using various event generators (NEUT, NuWro, ACHILLES) have failed to find a single model capable of simultaneously describing all MicroBooNE data, particularly regarding transverse kinematic imbalance (TKI) observables.

Methodology
This work utilizes the GENIE event generator (version 3.6.2, AR23 configuration) to benchmark state-of-the-art theoretical and empirical models against recent MicroBooNE CC0$\pi$ measurements, including those with multiple detected protons. The study leverages GENIE's flexible architecture to interchange specific model components one at a time, allowing for controlled comparisons between widely used empirical models and more theoretically sophisticated alternatives.

The study focuses on three primary model ingredients:

1. Nuclear Ground State Models: Comparing a modified Local Fermi Gas (LFG) model (inspired by spectral function approaches but using empirical momentum and binding energy) against a full Spectral Function (SF) model derived from fits to Jefferson Lab (e, e'p) data.
2. Nucleon Axial-Vector Form Factor: Comparing a fit to neutrino-deuterium data ($F_A^{\text{Deu}}$) against results from recent lattice quantum chromodynamics (LQCD) calculations ($F_A^{\text{LQCD}}$).
3. Hadronic Final-State Interactions (FSI): Comparing the default, data-driven empirical hA2018 model against the more theoretical Liège intranuclear-cascade (INCL v6.33.1) model.

Additionally, the authors address a known implementation error in the Nieves et al. QE cross-section model present in GENIE v3.6.2 and prior versions. This error, which arises from an incorrect frame transformation for off-shell nucleons, underestimates the cross-section (by $\sim$8% for SF models). The authors apply a correction to the code to ensure theoretical consistency. Random Phase Approximation (RPA) corrections are omitted for most custom configurations to maintain consistency between the LFG and SF models, as the standard RPA recipe is incompatible with the SF approach; the impact of RPA is noted to be small (<10%) for the MicroBooNE data.

Key Contributions and Results
The paper systematically evaluates combinations of these models against MicroBooNE data using $\chi^2$ and p-value metrics. Key findings include:

• Best-Performing Configuration: The models yielding the best agreement with MicroBooNE data combine the empirical hA2018 FSI model with the LQCD axial form factor ($F_A^{\text{LQCD}}$), paired with either the Nieves/LFG or SF nuclear models. These configurations achieve $\chi^2$/bin values less than 1.
• Axial Form Factor Sensitivity: The choice of axial form factor is identified as the most significant contributor to $\chi^2$ improvement. The LQCD-based form factor consistently provides a better fit than the traditional neutrino-deuterium fit ($F_A^{\text{Deu}}$), despite the latter being the basis for many years of simulations.
• FSI Model Performance: Contrary to expectations that more theoretical models would perform better, the empirical hA2018 FSI model consistently outperforms the theoretical INCL model. The INCL model, which includes effects like nucleon cluster formation, produces significantly worse fits to the data.
• Nuclear Model Sensitivity: The data show limited sensitivity to the details of the nuclear ground state; the Nieves/LFG and SF models yield similar $\chi^2$ values when paired with the same FSI and form factor models.
• MEC Model Impact: Variations in the MEC model (comparing SuSAv2, Valencia, and Martini et al.) produce significantly smaller differences in predictions (approx. 1/3 the magnitude) compared to the switch between axial form factors. The data cannot fully discriminate between the available MEC models.
• Comparison to Reference Models: The best-performing custom configurations provide a better fit to MicroBooNE data than the standard AR23 configuration or the "MicroBooNE Tune" (which relies on empirical scaling of the QE cross-section). The study suggests that using the $F_A^{\text{LQCD}}$ form factor offers a physically motivated way to achieve the necessary QE cross-section enhancement for heavier targets like argon, without relying solely on empirical tuning.

Significance
This work provides a detailed benchmark for upcoming argon-based neutrino experiments by isolating the impact of specific model ingredients within a single, flexible simulation framework. The authors claim that their results offer a "reasonable way" to produce the QE cross-section enhancement required by data through the adoption of LQCD form factors, rather than purely empirical scaling. Furthermore, the study highlights that while traditional observables (like muon and proton momentum distributions) are less specialized than TKI variables, they possess similar sensitivity for discriminating between these specific model variations. The paper concludes that while the SF nuclear model is preferred in electron scattering fits, the MicroBooNE data currently favor the LQCD axial form factor and the hA2018 FSI model, providing a concrete path forward for improving simulation accuracy in the GeV energy region.